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Proof step 429 from proof inv-rename-file-dentry (previous step)

files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(files, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ synced (files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)], icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], pcache), entries[str0] ∈ dirs0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 430:
⊦ synced(files, icache, pcache) → (¬ synced(files0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0)))
Proof step 431:
dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), synced(files, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ∀ ino. (ino ∈ files → synced(ino, icache0, pcache)) → ino ∈ files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)] → synced (ino, icache0[m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1))] [entries[str0], mkientry(false, mkinode(entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], pcache)

Rule argument

spec: cache-base name: synced-files-variant1 seq: ⊦ synced(files, icache, pcache) → ( ¬ synced(files0, icache0, pcache0) ↔ ¬ (∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0))) subst: [files, icache, pcache, files0, icache0, pcache0] → [files, icache0, pcache, files [entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content) ], icache0 [m3, mkientry (false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1)) ] [entries[str0], mkientry (false, mkinode (entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], pcache] flags: <all paths>

Additional information

Used terms: files, icache0, pcache, files [entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content) ], icache0 [m3, mkientry(false, mkinode(m3, md2, true, # links(m3, dirs0), m4, m1)) ] [entries[str0], mkientry (false, mkinode (entries[str0], md3, false, # links(entries[str0], dirs0), 0, m)) ], pcache